講演者：Ricardo Monti 氏（Gatsby Unit, University College London）
題 目：「Causal Discovery with General Non-Linear Relationships using Non-Linear ICA」
概要：We consider the problem of inferring causal relationships between two or more passively observed variables. While the problem of such causal discovery has been extensively studied especially in the bivariate setting, the majority of current methods assume a linear causal relationship, and the few methods which consider non-linear dependencies usually make the assumption of additive noise. Here, we propose a framework through which we can perform causal discovery in the presence of general non-linear relationships. The proposed method is based on recent progress in non-linear independent component analysis and exploits the non-stationarity of observations in order to recover the underlying sources or latent disturbances. We show rigorously that in the case of bivariate causal discovery, such non-linear ICA can be used to infer the causal direction via a series of independence tests. We further propose an alternative measure of causal direction based on asymptotic approximations to the likelihood ratio, as well as an extension to multivariate causal discovery. We demonstrate the capabilities of the proposed method via a series of simulation studies and conclude with an application to neuroimaging data.
講演者：Wenkai Xu 氏（Gatsby Unit, University College London）
題 目：「Community and Relational Detection via Structured Non-negative Factorisation」
概要：We propose a new method for community detection in directed networks. The proposed method identifies the communities based on directed interactions between them. Simultaneously, the method summarises these interactions by the directed edges between communities. The community assignment criteria are based on maximizing the net flow of (weighted) directed edges from one community to another. We show that in the absence and presence of noise, positive values in decomposed vectors of adjacency matrices are useful to identify communities and motivate our structured non-negative models. We present the multiplicative update algorithm for our model and show normalisation facilitates better convergence. In addition, we extend our model to a tensor version to tackle multiple network problem, that we identify communities with common structure and interactions between such communities, with multiple networks observed over the same set of vertices. For instance, in a social network, we observe different relationships such as "like", "hatred", "respect", etc. between users.